A Brief Introduction to Variational Integrators
A Brief Introduction to Variational Integrators
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变分积分器简介
DOI：
--
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Pablo Mata A
中科院分区：
文献类型：
--
作者：
A. Lew;Pablo Mata A
在这一章中，简要介绍了有限维拉格朗日系统的变分方法的制定。为此，前两节集中描述了拉格朗日和哈密顿观点的力学系统演变的流形。特别注意的是拉格朗日函数的建设和汉密尔顿的变分原理的平衡方程的推导中的作用。拉格朗日函数的对称性和不变量的动力学沿着与流动的辛性质的存在之间的关系也得到了解决。在第三部分，讨论转向制定的时间离散模拟的理论。这样一个建设的基石是由离散模拟的汉密尔顿的变分原理，它提供了一个系统的程序来构建离散近似的精确轨迹的机械系统的配置空间和相空间。的近似性质和所得到的离散轨迹的几何特性进行了解释。最后，我们应用变分方法来构造辛和动量守恒的时间积分的工程和科学的实际利益的两个问题。
In this chapter, a brief introduction to the formulation of variational methods for finite-dimensional Lagrangian systems is presented. To this end, the first two sections focus on describing the Lagrangian and Hamiltonian points of view of mechanics for systems evolving on manifolds. Special attention is paid to the construction of the Lagrangian function and to the role of Hamilton’s variational principle in the deduction of the balance equations. The relation between the symmetries of the Lagrangian function and the existence of invariants of the dynamics along with the symplectic nature of the flow are also addressed. In the third section, the discussion turns towards the formulation of a time-discrete analogue of the theory. The cornerstone of such a construction is given by a discrete analogue of Hamilton’s variational principle which provides a systematic procedure to construct discrete approximations to the exact trajectory of a mechanical system on both the configuration space and the phase space. The approximation properties and the geometric characteristics of the resulting discrete trajectories are explained. Finally, we apply the variational methodology to construct symplectic and momentum-conserving time integrators for two problems of practical interest in engineering and science.
用于复杂多体碰撞的不连续变分时间积分器
影响因子：
2.9
作者：
G. Johnson;S. Leyendecker;M. Ortiz
通讯作者：
M. Ortiz
非线性热机械问题的能量一致混合时空伽辽金方法
DOI：
10.1002/pamm.200610202
发表时间：
2006
期刊：
PAMM
影响因子：
--
作者：
Groß M;Betsch P.
通讯作者：
Betsch P.